Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands

Abstract

Moiré superlattices engineer band properties and enable observation of fractal energy spectra of Hofstadter butterfly. Recently, correlated-electron physics hosted by flat bands in small-angle moiré systems has been at the foreground. However, the implications of moiré band topology within the single-particle framework are little explored experimentally. An outstanding problem is understanding the effect of band topology on Hofstadter physics, which does not require electron correlations. Our work experimentally studies Chern state switching in the Hofstadter regime using twisted double bilayer graphene (TDBG), which offers electric field tunable topological bands, unlike twisted bilayer graphene. Here we show that the nontrivial topology reflects in the Hofstadter spectra, in particular, by displaying a cascade of Hofstadter gaps that switch their Chern numbers sequentially while varying the perpendicular electric field. Our experiments together with theoretical calculations suggest a crucial role of charge polarization changing concomitantly with topological transitions in this system. Layer polarization is likely to play an important role in the topological states in few-layer twisted systems. Moreover, our work establishes TDBG as a novel Hofstadter platform with nontrivial magnetoelectric coupling.

Aligned Bamboo Fiber‐Induced Crystallinity Mitigation of Lightweight Polymer Composite Enables Ultrahigh Strength and Unprecedented Toughness

“…This is because the fillers’ orientation can overlap with the applied stress direction, allowing for effective stress dissipation. [ 14 ] Emerging techniques, such as electrospinning, [ 15 ] melt extrusion, [ 16 ] and electric/magnetic field inductions, [ 17 ] have been used to provide an aligned filler in the polymer matrix. However, these techniques face two significant obstacles: (i) As a result of the limited interfacial bonding between the fibers and the polymer chain, the potential reduction in the crystallinity of the polymer matrix remains insufficient.…”

Emerging Characteristics and Properties of Moiré Materials

“…This is a noteworthy advancement in the field [16,33,34]. The atomic and electronic structure of vdW heterostructures is subject to periodic modulation by Moiré superlattices (MSLs), leading to the appearance of several phenomena such as the formation of shear solitons and topological point defects [35][36][37][38], secondary Dirac cones [39][40][41], and Hofstadter butterfly states [33,[42][43][44]. In addition, flat bands were discussed back in 2011; such flat energy bands are of interest and may localize the presence of electronic states.…”

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice

“…So far, in graphene moireś ystems, by increasing carrier density the total Chern number of all populated flavors may vary from one to four, 8−14 Chern number of the nondegenerate band itself remains unchanged; Multiple layers of Chern insulators such as Crdoped Bi 2 (Se,Te) 3 /Bi 2 (Se,Te) 3 and MnBi 2 Te 4 have been physically stacked to achieve a predesigned Chern number, 55−57 which nevertheless cannot be changed any more. The electric field control of Chern numbers, similar to the tuning of Hofstadter subbands, 58,59 calls for more theoretical and experimental exploration. Rhombohedral trilayer graphene moirésuperlattices, 21,60−62 made by zero-degree alignment between graphene and boron nitride which is energetically favorable to suppress the twistangle disorder, provide a robust platform to realize valley polarization and examine how electric field tunes the Chern number of a topological band.…”

“…So far, in graphene moiré systems, by increasing carrier density the total Chern number of all populated flavors may vary from one to four, − but the Chern number of the nondegenerate band itself remains unchanged; Multiple layers of Chern insulators such as Cr-doped Bi 2 (Se,Te) 3 /Bi 2 (Se,Te) 3 and MnBi 2 Te 4 have been physically stacked to achieve a predesigned Chern number, − which nevertheless cannot be changed any more. The electric field control of Chern numbers, similar to the tuning of Hofstadter subbands, , calls for more theoretical and experimental exploration.…”